Shear force & bending moment worksheet with answers

Free printable Shear force & bending moment worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
P = 35 kNABsection1 m9 m

Find the bending moment Mx at the section x = 1 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 10 mP = 35 kN at 1 mx = 1 m
Mx = kN·m
2.Easy
P = 40 kNAB3 m5 m

The simply supported beam carries a single point load P. Find the shear force Vx just to the right of the load. Use sagging moments positive and upward shear on the left face positive.

L = 8 mP = 40 kN at 3 m
Vx = kN
3.Medium
P1​ = 35 kNP2​ = 65 kNAB3 m1.5 m1.5 m

The simply supported beam carries two point loads. Find the maximum bending moment Mmax in the beam.

L = 6 mP1 = 35 kN at 3 mP2 = 65 kN at 4.5 m
Mmax = kN·m
4.Medium
w = 4 kN/mABsection3.5 m2.5 m

Find the shear force Vx at the section x = 3.5 m from support A. Use sagging moments positive and upward shear on the left face positive.

L = 6 mw = 4 kN/m from 0 to 6 mx = 3.5 m
Vx = kN
5.Hard
55 kN20 kNABCDEFG2 m2 m2 m2 m2 m2 m

The marks A to G split the beam into six equal parts. At which mark is the bending moment largest in size, sagging or hogging? Click it in the diagram.

55 kN @ 12 m20 kN @ 4 m
  1. 1A (x = 0 m)
  2. 2B (x = 2 m)
  3. 3C (x = 4 m)
  4. 4D (x = 6 m)
  5. 5E (x = 8 m)
  6. 6F (x = 10 m)
  7. 7G (x = 12 m)
6.Hard
w = 6 kN/mABC8 m2 m

The beam rests on a pin at A and a roller at B and overhangs B by 2 m to the free end C. A uniformly distributed load w acts over the whole length A–C. Find the maximum sagging bending moment Mmax between the supports.

L = 10 mw = 6 kN/m from 0 to 10 msupports at x = 0 and x = 8 m
Mmax = kN·m

Answer key

  1. 1. Mx = 31.5 kN·m
  2. 2. Vx = −15 kN
  3. 3. Mmax = 101.3 kN·m
  4. 4. Vx = −2 kN
  5. 5. F (x = 10 m)
  6. 6. Mmax = 42.19 kN·m

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